Arrange the following compounds in order of their reactivity towards `S_N2` reaction
(i) `CH_3(CH_2)_3CH_2Br`
(ii) `(CH_3)_2CHCH_2CH_2Br`
(iii) `CH_(3)CH_(2)-overset(CH_(3))overset("| ")"CH"-CH_(2)Br`

Options

A. `(i) gt (iii) gt (ii)`
B. `(ii) gt (iii) gt (i) `
C. `(iii) gt (i) gt (ii)`
D. `(ii) gt (i) gt (iii) `

Answer

To determine the order of reactivity of the given compounds towards the \( S_N2 \) reaction, we need to analyze the structure of each compound and their steric hindrance. The \( S_N2 \) mechanism favors less steric hindrance, allowing the nucleophile to attack the electrophilic carbon more easily.

### Step-by-Step Solution:

1. **Identify the Structures of the Compounds**:
- (i) \( CH_3(CH_2)_3CH_2Br \): This is a primary alkyl bromide.
- (ii) \( (CH_3)_2CHCH_2CH_2Br \): This is a secondary alkyl bromide.
- (iii) \( CH_3CH_2-CH(CH_3)-CH_2Br \): This is also a secondary alkyl bromide.

2. **Determine the Type of Alkyl Halides**:
- Primary alkyl halides (like compound (i)) have the least steric hindrance, making them more reactive in \( S_N2 \) reactions.
- Secondary alkyl halides (like compounds (ii) and (iii)) have more steric hindrance compared to primary alkyl halides, which decreases their reactivity in \( S_N2 \) reactions.

3. **Rank the Reactivity**:
- Since \( S_N2 \) reactions are favored by less steric hindrance, we can rank the compounds based on their structure:
- Compound (i) \( CH_3(CH_2)_3CH_2Br \) (primary) will be the most reactive.
- Between compounds (ii) and (iii), both are secondary, but we need to consider their structures:
- Compound (ii) \( (CH_3)_2CHCH_2CH_2Br \) has a more branched structure compared to compound (iii) \( CH_3CH_2-CH(CH_3)-CH_2Br \), which makes (ii) slightly less reactive than (iii).
- Therefore, the order of reactivity is:
- (i) > (iii) > (ii)

4. **Final Order**:
- The final order of reactivity towards \( S_N2 \) reaction is:
- **(i) > (iii) > (ii)**

### Conclusion:
The correct order of reactivity towards \( S_N2 \) reaction is:
- **(i) \( CH_3(CH_2)_3CH_2Br \) > (iii) \( CH_3CH_2-CH(CH_3)-CH_2Br \) > (ii) \( (CH_3)_2CHCH_2CH_2Br \)**.